Context. Modern radio astronomical arrays have (or will have) more than one
order of magnitude more receivers than classical synthesis arrays, such as the
VLA and the WSRT. This makes gain calibration a computationally demanding task.
Several alternating direction implicit (ADI) approaches have therefore been
proposed that reduce numerical complexity for this task from O(P3)
to O(P2), where P is the number of receive paths to be
calibrated.
Aims. We present an ADI method, show that it converges to the optimal
solution, and assess its numerical, computational and statistical performance.
We also discuss its suitability for application in self-calibration and report
on its successful application in LOFAR standard pipelines.
Methods. Convergence is proved by rigorous mathematical analysis using a
contraction mapping. Its numerical, algorithmic, and statistical performance,
as well as its suitability for application in self-calibration, are assessed
using simulations.
Results. Our simulations confirm the O(P2) complexity and
excellent numerical and computational properties of the algorithm. They also
confirm that the algorithm performs at or close to the Cramer-Rao bound (CRB,
lower bound on the variance of estimated parameters). We find that the
algorithm is suitable for application in self-calibration and discuss how it
can be included. We demonstrate an order-of-magnitude speed improvement in
calibration over traditional methods on actual LOFAR data.
Conclusions. In this paper, we demonstrate that ADI methods are a valid and
computationally more efficient alternative to traditional gain calibration
method and we report on its successful application in a number of actual data
reduction pipelines.Comment: accepted for publication in Astronomy & Astrophysic